Billionaire investor Carl Icahn wants eBay to spin-off its surging PayPal unit. On Wednesday, eBay said its board considered Icahn’s proposal and rejected it, setting the stage for a potential showdown between the technology giant and the 77-year-old investor. PayPal is eBay’s fastest-growing division and accounts for an increasing amount of the company’s revenue. Icahn thinks an independent PayPal will be able to grow even faster than it has thanks to an ongoing boom in online-payments. And in a conversation with TIME, he suggested that he might even see a connection between his new assault on eBay and one of his other pet projects: Apple. A lightly edited transcript follows.

What is your strategy here?

I believe strongly in corporate governance. Very simply, the strategy is to start by putting up two candidates. These precatory [filings] have a lot more teeth than they used to. If 51% of shareholders vote for our proposal, the board is going to have a tough time holding out. They don’t have to, legally, but it will be very difficult. That’s why we don’t need a 10% to 15% stake; we can be more efficacious if we win the precatory.

You hold less than 1% of the stock, making you the 25th largest outside shareholder. Do you plan to keep accumulating shares? Have you already bought more?

Anything is possible. But I don’t think it’s that important here. What matters is what happens with the precatory.

Ultimately, what do you see PayPal becoming in the future?

PayPal is a growth company growing at a much better rate than eBay. PayPal is a gem. eBay is eBay; it’s not going to get hurt. eBay can still have a contract with PayPal, but PayPal can be out there with a higher multiple. I think the value would be up right away. Within a couple of months, with a good board, I think you’d have two or three serious suitors. Apple, Google, Mastercard and Discover, for example. I did this when we split Reynolds Tobacco from Nabisco: the stock not only went up but Philip Morris bought Nabisco.

You’ve said you want to nominate two directors. Have you identified two existing ones you’d like to see go?